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C₂×#12751 #493555

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4)(5,16,20,44)(6,22,25,40)(7,27)(8,13)(9,15)(10,18,34,50)(11,24,36,26)(12,29)(14,31)(17,45)(19,43,21,37)(23,55,58,35)(28,41,51,33)(30,38)(32,60)(39,49)(42,52)(46,61)(47,65)(48,64)(53,66)(54,57,63,59)(56,62);(3,5)(4,10)(6,17)(7,28)(8,19)(9,20)(11,32)(12,37)(13,33)(14,41)(15,34)(16,38)(18,49)(21,31)(22,53)(23,56)(24,47)(25,48)(26,52)(27,44)(29,50)(30,51)(35,45)(36,62)(39,43)(40,61)(42,63)(46,57)(54,65)(55,64)(58,60)(59,66);(3,6,9,25)(4,11,15,36)(5,17,20,48)(7,23,30,58)(8,26,31,24)(10,32,34,62)(12,35,39,55)(13,40,14,22)(16,42,44,65)(18,46,50,66)(19,52,21,47)(27,54,38,63)(28,56,51,60)(29,59,49,57)(33,61,41,53)(37,45,43,64)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400751);